As for a crystal resonator of an AT cut often used for a crystal oscillator, it is known that a temperature change against a fixed natural resonance frequency is represented by an approximate cubic function as shown in FIG. 17. And this temperature characteristic can be approximated as formula (1) below.Y=α(t−t0)3β(t−t0)+γ  (1)Here, Y is an output frequency, α is a cubic coefficient, β is a inclination of a temperature characteristic, γ is a frequency at t0, and t0 is a central temperature of a curve, that is, an inflection point (normally, a range from 25 to 30° C.). Each of α, β and γ of the above formula (1) greatly depends on the crystal resonator.
For this reason, temperature compensation has been conventionally performed by using an output voltage from an approximate cubic function generating device as described in U.S. Pat. No. 3,233,946 for instance.
To be more specific, as shown in FIG. 18, the output of the approximate cubic function generating device for generating the approximate cubic function is supplied to a voltage-controlled crystal oscillator (VCXO) as a control voltage for compensating for the temperature characteristic of crystal, the device using a voltage VIN outputted from a temperature detecting circuit for outputting a voltage changing primarily against the temperature change as an input signal.
A voltage-frequency characteristic of the voltage-controlled crystal oscillation circuit widely applied at present can be approximated by a linear function. Therefore, the frequency characteristic against the temperature of the crystal resonator can be approximated by a voltage characteristic against the temperature as shown in FIG. 19.
A voltage-temperature characteristic of the control voltage will be as in the following formula (2).f(t)=a3(t−t0)3+a1(t−t0)+a0  (2)To be more specific, the voltage matching the control voltage in formula (2) is generated by the approximate cubic function generating device and is inputted to the voltage-controlled crystal oscillator so as to compensate for the temperature characteristic of the crystal resonator.
However, a frequency-temperature characteristic of the crystal resonator includes an order component larger than a cubic component. Therefore, there is a difference between an approximate cubic function and data so that, even if the control voltage capable of strictly compensating for the approximate cubic function is generated, this difference remains as an element for being incapable of temperature compensation.
To solve this, it is possible to approximate the temperature characteristic of the crystal resonator with a function of a higher order and control the voltage-controlled crystal oscillator with a voltage of a function of a high order corresponding thereto so as to reduce the difference.
For instance, in the case of approximating frequency-temperature characteristic data on one crystal resonator with a cubic function, the difference between an approximate expression and the data is 0.320 ppm at the maximum in a temperature range of −30 to 85° C. If this is approximated with a function of a fourth order, it becomes 0.130 ppm. And if further approximated with a function of a fifth order, it becomes 0.126 ppm. It is thus possible to adjust the coefficient and generate the control voltage by using a device for generating the functions of higher orders so as to perform the temperature compensation with a higher order of accuracy.
As for a circuit for outputting a signal proportional to the functions cubic or of higher orders so far, a function generating device shown in FIG. 1 of Japanese Patent Laid-Open No. 8-116214 is known for instance.
The signal outputted from this circuit can be represented as a polynomial such as formula (3) below which is a general expression.
                                                                        f                ⁡                                  (                  x                  )                                            =                                                                    a                    n                                    ⁢                                      x                    n                                                  +                                                      a                                          n                      -                      1                                                        ⁢                                      x                                          n                      -                      1                                                                      +                …                +                                                      a                    2                                    ⁢                                      x                    2                                                  +                                                      a                    1                                    ⁢                  x                                +                                  a                  0                                                                                                        =                                                                                          a                      n                      ′                                        ⁡                                          (                                              x                        -                                                  x                          0                                                                    )                                                        n                                +                …                +                                                      a                    1                    ′                                    ⁡                                      (                                          x                      -                                              x                        0                                                              )                                                  +                                  a                  0                  ′                                                                                        (        3        )            For instance, an output signal of a fourth order function generating device can be represented by formula (4) below.
                                                                        f                ⁡                                  (                  x                  )                                            =                                                                    a                    4                                    ⁢                                      x                    4                                                  +                                                      a                    3                                    ⁢                                      x                    3                                                  +                                                      a                    2                                    ⁢                                      x                    2                                                  +                                                      a                    1                                    ⁢                  x                                +                                  a                  0                                                                                                        =                                                                                          a                      4                      ′                                        ⁡                                          (                                              x                        -                                                  x                          0                                                                    )                                                        4                                +                                                                            a                      2                      ′                                        ⁡                                          (                                              x                        -                                                  x                          0                                                                    )                                                        2                                +                                                      a                    1                                    ⁡                                      (                                          x                      -                                              x                        0                                                              )                                                  +                                  a                  0                  ′                                                                                        (        4        )            However,    a4′=a4a2′=a2−6a4x02, a1′=a1+2a2x0−8a4x03, a0′=a0+a1x0+a2x02−3a4x04, x0=−a3/(4a4)
As for the approximate fourth order function generating device, it is possible, by using x0 as in the above formula (4), to omit an n−1st term, that is a cubic term and also reduce a circuit size.
However, the conventional example has an unsolved problem that it is difficult to implement the circuit for generating the control voltage with a configuration as in the formula (4).
The unsolved problem will be described by using a concrete example. If the frequency-temperature characteristic data on one crystal resonator is described first as a formula having the cubic term omitted as the formula (4), to representing the inflection point of this function becomes −149° C. to significantly exceed the normally compensated range of −30 to 85° C. A significant deviation of to means that the circuit must have a wide input range of a functional circuit for generating the control voltage equivalent thereto and must be the circuit having the temperature outside an adjustment range taken into consideration. FIG. 20 shows the order components, where it is understandable that, while the frequency-temperature characteristic of one crystal resonator is within ±10 ppm, the order components have the functions a significant deflection width of ±1500 ppm at the maximum added thereto. Therefore, to compensate for the frequency-temperature characteristic of the crystal resonator, the adjustment range of the coefficients a4′ to a0′ of the orders must be wide for the control voltage, and the circuit for implementing this becomes very disadvantageous as a dynamic range. Consequently, there arise the problems of significant increase in noise and expansion of the circuit size due to extension of the control voltage from the cubic function to the function of the fourth order. Thus, it is not practical even when considering a merit of obtaining a higher order of accuracy.
Consequently, the present invention has been implemented by noting the unsolved problems of the conventional example. And an object thereof is to provide the circuit capable of accurately providing high order components which are cubic or of higher orders and an accurately adjustable crystal oscillator using the function generating device thereof for the temperature compensation.